单纯随机抽样理论之我见

针对一般经济统计教材中普遍存在的关于单纯随机抽样过程中,不同抽样方法下样本方差的无偏性问题提出自己的见解.认为,抽样理论源于实践,重复抽样时有Nn个样本、不重复抽样时有CnN个样本是实际抽样调查工作中普遍采用的方式、方法,更是单纯随机抽样推断理论的源泉.在此基础上数学界将实际工作中各种可能始点的抽样方法赋予理性思考、研究,获得结论:无限制抽样和简单随机抽样条件下样本方差是总体方差的无偏估计量.     

Geometry of regular modules over canonical algebras

We classify canonical algebras such that for every dimension vector of a regular module the corresponding module variety is normal (respectively, a complete intersection). We also prove that for the dimension vectors of regular modules normality is equivalent to irreducibility.

     

Determination of 5‐fluorocytosine, 5‐fluorouracil,and 5‐fluorouridine in hospital wastewater by liquid chromatography–mass spectrometry

Chemotherapeutics are pharmaceutical compounds the occurrence of which in the environment is of growing concern because of the increase in treatments against cancer diseases. They can reach the aquatic ecosystems after passing through wastewater treatment plants without complete removal. One of the most frequently used chemotherapeutics is 5‐fluorouracil which exhibits a strong cytostatic effect. In this paper, an analytical methodology was developed, validated, and applied to determine 5‐fluorouracil, its precursor, 5‐fluorocytosine, and its major active metabolite, 5‐fluorouridine, in hospital wastewater samples. Due to the expected low concentrations after dilution and interferences present in such a complex matrix, a very selective and sensitive detection method is required. Moreover, an extraction method must be implemented prior to the determination in order to purify the sample extract and preconcentrate the target analytes at micrograms per liter concentration levels. Solid‐phase extraction followed by liquid chromatography with tandem mass spectrometry was the combination of choice and all included parameters were studied. Under optimized conditions for wastewater samples analysis, recoveries from 63 to 108% were obtained, while intraday and interday relative standard deviations never exceeded 20 and 25%, respectively. Limits of detection between 61 and 620 ng/L were achieved. Finally, the optimized method was applied to samples from hospital wastewater effluents.     

Application of simultaneous separation and derivatization for the determination of α‐lipoic acid in urine samples by high‐performance liquid chromatography with spectrofluorimetric detection

To help to clarify therapeutic functions of lipoic acid (LA) in biochemical and clinical practice we have elaborated a fast, simple and accurate HPLC method enabling determination of LA in human urine. The proposed analytical approach includes reduction of LA with tris(2‐carboxyethyl)phosphine and simultaneous separation and derivatization of the analyte with butylamine and o‐phthaldialdehyde followed by spectrofluorimetric detection at λ_ex = 340 nm and λ_em = 440 nm. The assay was performed using gradient elution and the mobile phase containing 0.0025 mol L^?1 o‐phthaldialdehyde in 0.0025 mol L^?1 NaOH and acetonitrile. Linearity of the detector response for LA was observed in the range of 0.3–8 μmol L^?1. Limits of detection and quantification for LA in urine samples were 0.02 and 0.03 μmol L^?1, respectively. The total analysis time, including sample work‐up, was <20 min. The analytical procedure was successfully applied to analysis of real urine samples delivered from six healthy volunteers who received a single 100 mg dose of LA.     

基于仿真优化的炼钢生产批调度求解方法

论文针对钢铁企业炼钢工序具有高温、高能耗、复杂工况的实际特征,从中提炼出生产批调度问题,其工件根据其实际工艺属性可分为多个簇,基于给定的工件簇,决策工件的分批和调度情况,综合考虑工件之间的切换费用,以及工件提前、拖期所导致的惩罚,使得总的生产成本期望最小化,从而降低生产成本;针对该问题,考虑工件的处理时间、工件的加工属性具有不确定性,基于仿真优化思想,建立数学模型,并基于大数定理,对模型目标函数进行近似;提出基于样本近似方法的求解框架,通过随机抽样的方法获得不同规模的样本,针对不同规模的样本,提出Filter & Fan算法对问题进行求解;最后,通过基于实际数据的计算实验验证所提算法的有效性。     

A remark on strong law of large numbers for weighted U-statistics

Let {X,Xn; n ≥ 1} be a sequence of i.i.d.random variables with values in a measurable space(S,S) such that E|h(X1,X2,...,Xm)| ∞,where h is a measurable symmetric function from Sminto R =(-∞,∞).Let {wn,i1,i2,...,im; 1 ≤ i1 i2 ··· im ≤ n,n ≥ m} be a matrix array of real numbers.Motivated by a result of Choi and Sung(1987),in this note we are concerned with establishing a strong law of large numbers for weighted U-statistics with kernel h of degree m.We show that lim n→∞m!(n-m)!n!1≤i1i2···im≤n wn,i1,i2,...,im(h(Xi1,Xi2,...,Xim)-θ)=0 a.s.whenever supn≥mmax1≤i1i2···im≤n|wn,i1,i2,...,im|∞,whereθ=Eh(X1,X2,...,Xm).The proof of this result is based on a new general result on complete convergence,which is a fundamental tool,for array of real-valued random variables under some mild conditions.     

Monotonicity properties of ‐functions

We present some monotonicity results for a class of Dirichlet series generalizing previously known results. The fact that is in that class presents a first example of an arithmetic function for which the associated Dirichlet series is completely monotonic, but not logarithmically completely monotonic. Lastly, we use similar techniques to prove another formulation of the Riemann hypothesis for the L‐function associated to the Ramanujan‐tau function.     

Significant difference in active metabolite levels of ginseng in humans consuming Asian or Western diet: The link with enteric microbiota

After ingestion of ginseng, the bioavailability of its parent compounds is low and enteric microbiota plays an important role in parent compound biotransformation to their metabolites. Diet type can influence the enteric microbiota profile. When human subjects on different diets ingest ginseng, their different gut microbiota profiles may influence the metabolism of ginseng parent compounds. In this study, the effects of different diet type on gut microbiota metabolism of American ginseng saponins were investigated. We recruited six healthy adults who regularly consumed different diet types. These subjects received 7 days' oral American ginseng, and their biological samples were collected for LC‐Q‐TOF‐MS analysis. We observed significant ginsenoside Rb₁ (a major parent compound) and compound K (a major active metabolite) level differences in the samples from the subjects consuming different diets. Subjects on an Asian diet had much higher Rb₁ levels but much lower compound K levels compared with those on a Western diet. Since compound K possesses much better cancer chemoprevention potential, our data suggested that consumers on a Western diet should obtain better cancer prevention effects with American ginseng intake compared with those on an Asian diet. Ginseng compound levels could be enhanced or reduced via gut microbiota manipulation for clinical utility.